{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10379","name":"Three Notes on Distributed Property Testing","abstract":"In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P means distinguishing graphs G = (V,E) having property P from graphs that are epsilon-far from having it, meaning that epsilon|E| edges must be added or removed from G to obtain a graph satisfying P.\r\n\r\nWe present a series of results, including:\r\n\r\n- Testing H-freeness in O(1\/epsilon) rounds, for any constant-sized graph H containing an edge (u,v) such that any cycle in H contain either u or v (or both). This includes all connected graphs over five vertices except K_5. For triangles, we can do even better when epsilon is not too small.\r\n\r\n- A deterministic CONGEST protocol determining whether a graph contains a given tree as a subgraph in constant time.\r\n\r\n- For cliques K_s with s >= 5, we show that K_s-freeness can be tested in O(m^(1\/2-1\/(s-2)) epsilon^(-1\/2-1\/(s-2))) rounds, where m is the number of edges in the network graph.\r\n\r\n- We describe a general procedure for converting epsilon-testers with f(D) rounds, where D denotes the diameter of the graph, to work in O((log n)\/epsilon)+f((log n)\/epsilon) rounds, where n is the number of processors of the network. We then apply this procedure to obtain an epsilon-tester for testing whether a graph is bipartite and testing whether a graph is cycle-free. Moreover, for cycle-freeness, we obtain a corrector of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property.\r\n\r\nThese protocols extend and improve previous results of [Censor-Hillel et al. 2016] and [Fraigniaud et al. 2016].","keywords":["Property testing","Property correcting","Distributed algorithms","CONGEST model"],"author":[{"@type":"Person","name":"Even, Guy","givenName":"Guy","familyName":"Even"},{"@type":"Person","name":"Fischer, Orr","givenName":"Orr","familyName":"Fischer"},{"@type":"Person","name":"Fraigniaud, Pierre","givenName":"Pierre","familyName":"Fraigniaud"},{"@type":"Person","name":"Gonen, Tzlil","givenName":"Tzlil","familyName":"Gonen"},{"@type":"Person","name":"Levi, Reut","givenName":"Reut","familyName":"Levi"},{"@type":"Person","name":"Medina, Moti","givenName":"Moti","familyName":"Medina"},{"@type":"Person","name":"Montealegre, Pedro","givenName":"Pedro","familyName":"Montealegre"},{"@type":"Person","name":"Olivetti, Dennis","givenName":"Dennis","familyName":"Olivetti"},{"@type":"Person","name":"Oshman, Rotem","givenName":"Rotem","familyName":"Oshman"},{"@type":"Person","name":"Rapaport, Ivan","givenName":"Ivan","familyName":"Rapaport"},{"@type":"Person","name":"Todinca, Ioan","givenName":"Ioan","familyName":"Todinca"}],"position":15,"pageStart":"15:1","pageEnd":"15:30","dateCreated":"2017-10-12","datePublished":"2017-10-12","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Even, Guy","givenName":"Guy","familyName":"Even"},{"@type":"Person","name":"Fischer, Orr","givenName":"Orr","familyName":"Fischer"},{"@type":"Person","name":"Fraigniaud, Pierre","givenName":"Pierre","familyName":"Fraigniaud"},{"@type":"Person","name":"Gonen, Tzlil","givenName":"Tzlil","familyName":"Gonen"},{"@type":"Person","name":"Levi, Reut","givenName":"Reut","familyName":"Levi"},{"@type":"Person","name":"Medina, Moti","givenName":"Moti","familyName":"Medina"},{"@type":"Person","name":"Montealegre, Pedro","givenName":"Pedro","familyName":"Montealegre"},{"@type":"Person","name":"Olivetti, Dennis","givenName":"Dennis","familyName":"Olivetti"},{"@type":"Person","name":"Oshman, Rotem","givenName":"Rotem","familyName":"Oshman"},{"@type":"Person","name":"Rapaport, Ivan","givenName":"Ivan","familyName":"Rapaport"},{"@type":"Person","name":"Todinca, Ioan","givenName":"Ioan","familyName":"Todinca"}],"copyrightYear":"2017","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.DISC.2017.15","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/dx.doi.org\/10.1007\/978-3-662-53426-7_3","http:\/\/arxiv.org\/abs\/1705.04898","http:\/\/arxiv.org\/abs\/1705.04033","http:\/\/arxiv.org\/abs\/1706.03996","http:\/\/dx.doi.org\/10.1145\/2332432.2332504","http:\/\/dx.doi.org\/10.1145\/2554797.2554843","http:\/\/dx.doi.org\/10.1006\/jagm.1998.0929","http:\/\/dx.doi.org\/10.1145\/2767386.2767398","http:\/\/dx.doi.org\/10.1016\/S0304-0208(08)73110-4","http:\/\/dx.doi.org\/10.1145\/2591796.2591850","http:\/\/dx.doi.org\/10.1007\/978-3-662-46078-8_31"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6294","volumeNumber":91,"name":"31st International Symposium on Distributed Computing (DISC 2017)","dateCreated":"2017-10-12","datePublished":"2017-10-12","editor":{"@type":"Person","name":"Richa, Andr\u00e9a","givenName":"Andr\u00e9a","familyName":"Richa"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10379","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6294"}}}